The electric power steering apparatus is a machine which operates the motor for generating the steering assist force according to a steering torque applied by a driver. The recent years have seen a fast-growing demand for electric power steering apparatuses for use in large cars. Such a large car requires an increased steering assist force so that a larger amount of electric power must be supplied to the motor. In some cases, however, a battery alone may be unable to fully meet such a large power demand. In this connection, an arrangement has been proposed wherein an auxiliary power supply is provided in addition to the battery such that the normal power demand is met by the battery alone but when a larger amount of electric power is required, the electric power is supplied by both the battery and the auxiliary power supply connected in series (see, for example, Japanese Unexamined Patent Publication No. 2005-287222 (FIG. 1)).
The hitherto known electric power steering apparatuses as described above may cause a control hunting if there are slight fluctuations of the required electric power in the vicinity of a threshold value as a boundary point between a mode in which the electric power is supplied by the battery alone and a mode in which the electric power is supplied by the combination of battery and auxiliary power supply.